Finite Group Databasebeta

← #20253587

Subgroups — #20253587

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689728C211yesmaximal, characteristic, complemented
2#15689441C211yesmaximal, characteristic, complemented
3#15689436C211yesmaximal, characteristic, complemented
4#15689430C211yesmaximal, characteristic, complemented
5#15689423C211yesmaximal, characteristic, complemented
6#15689323C211yesmaximal, characteristic, complemented
7#15689318C211yesmaximal, characteristic, complemented
8#15689268C211yesmaximal, characteristic, complemented
9#15689268C211yesmaximal, characteristic, complemented
10#15689233C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12C4×#10625336C211yesmaximal, characteristic, complemented
13C4×#10625334C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#520C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20#13094021C2211yescharacteristic
21#13094016C2211yescharacteristic
22#13094009—21no—
23#13094009—21no—
24#13093998C2211yescharacteristic
25#13093998C2211yescharacteristic
26#13093997—21no—
27#13093997—21no—
28C4×D188C2211yescharacteristic
29C4×D188C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093944C2211yescharacteristic
41#13093944C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C4×Q8×C47C2211yescharacteristic
50C4×Q8×C47C2211yescharacteristic
51C4×D4×C47—21no—
52C4×D4×C47—21no—
53C4×D4×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#117×C47—21no—
56#117×C47C2211yescharacteristic
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—22no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188C2311yescharacteristic
74C2×D188C2311yescharacteristic
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47D411yescharacteristic
81C4⋊C4×C47D411yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47D411yescharacteristic
87C22⋊C4×C47D411yescharacteristic
88C42×C47—21no—
89C42×C47—21no—
90C42×C47C2311yescharacteristic
91C42×C47C2311yescharacteristic
92#10625336—22no—
93#10625336—22no—
94#10625334—22no—
95#10625334—22no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111C22×D47—21no—
112Q8×C47—21no—
113Q8×C47#4112yes—
114D4×C47—24no—
115D4×C47—21no—
116D4×C47#4112yes—
117C2×C4×C47—24no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—81no—
124C2×C4×C47—81no—
125C2×C4×C47—81no—
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—81no—
133C22⋊D47—81no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136D188—21no—
137D188—21no—
138D188—21no—
139D188—21no—
140D188—81no—
141D188—81no—
142C4×D47—81no—
143C4×D47—81no—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—22no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47C22×D411yescharacteristic
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C4×C47—21no—
162C4×C47—22no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47C2×#4111yescharacteristic
171Dic47—41no—
172Dic47—41no—
173#3119—471nomaximal, Sylow
174C2×C47—41no—
175C2×C47—42no—
176C2×C47#52511yescharacteristic
177C2×C47#57611yescharacteristic
178C2×C47#57711yescharacteristic
179D47—81no—
180D47—81no—
181#540—471no—
182#520D4711yescharacteristic, complemented
183#481—471no—
184#480—471no—
185#479—471no—
186#478—471no—
187#460—471no—
188#459—471no—
189#449—471no—
190#449—471no—
191#442—471no—
192#440—471no—
193C4×SD16—471no—
194C4×D8—471no—
195#433—471no—
196C47#311911yescharacteristic, complemented, Sylow
197C2×#41C2×D4711yescharacteristic
198C2×SD16—471no—
199C2×SD16—471no—
200C2×D8—471no—
201C2×D8—471no—
202#127—471no—
203#125—471no—
204#123—941no—
205#123—941no—
206#121—471no—
207#121—471no—
208#121—941no—
209#121—941no—
210C4×Q8C2×D4711yescharacteristic
211C4×Q8C2×D4711yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4C2×D4711yescharacteristic
217C4×D4C2×D4711yescharacteristic
218#117—21no—
219#117C2×D4711yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D4711yescharacteristic
222#107—471no—
223#107—471no—
224#106—471no—
225#106—471no—
226C4⋊C8—471no—
227C4⋊C8—471no—
228#103—471no—
229#103—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236C22⋊C8—471no—
237C22⋊C8—471no—
238#97—471no—
239C4×C8—471no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D4711yescharacteristic
243C2×D4—21no—
244C2×D4—471no—
245C2×D4—471no—
246C2×D4—941no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4—941no—
250C2×D4C22×D4711yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258SD16—942no—
259SD16—942no—
260D8—942no—
261D8—942no—
262C2×C8—471no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8—471no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22⋊D4711yescharacteristic
274C4⋊C4C22⋊D4711yescharacteristic
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4C22⋊D4711yescharacteristic
284C22⋊C4C22⋊D4711yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D4711yescharacteristic
288C42C22×D4711yescharacteristic
289C23—21no—
290C23—941no—
291C23—941no—
292C23C2×C22⋊D4711yescharacteristic
293Q8—21no—
294Q8#1062535012yes—
295D4—24no—
296D4—21no—
297D4—941no—
298D4—941no—
299D4—941no—
300D4—941no—
301D4—3761no—
302D4—3761no—
303D4—3761no—
304D4—3761no—
305D4#1062535012yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—3761no—
318C2×C4—3761no—
319C2×C4C2×C22⋊D4711yescharacteristic
320C2×C4C2×C22⋊D4711yescharacteristic
321C2×C4C2×C22⋊D4711yescharacteristic
322C2×C4C2×C22⋊D4711yescharacteristic
323C2×C4C2×C22⋊D4711yescharacteristic
324C2×C4C23×D4711yescharacteristic
325C8—941no—
326C8—941no—
327C8—941no—
328C8—941no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—1881no—
336C22—1881no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22—1881no—
341C22C22×C22⋊D4711yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—1881no—
351C4—1881no—
352C4C2×#1062535011yescharacteristic
353C4C2×#1062535011yescharacteristic
354C2—41no—
355C2—42no—
356C2—3761no—
357C2—3761no—
358C2#1568963411yescharacteristic
359C2#1568992611yescharacteristic
360C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#520C2
socleC22×C47C22×D4
hypercenter#520D47
hypocenterC47#3119
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689728C2semidirect
2. #15689441C2semidirect
3. #15689436C2semidirect
4. #15689430C2semidirect
5. #15689423C2semidirect
6. #15689323C2semidirect
7. #15689318C2semidirect
8. #15689268C2semidirect
9. #15689268C2semidirect
10. #15689233C2semidirect
11. #15689221C2semidirect
12. C4×#10625336C2semidirect
13. C4×#10625334C2semidirect
14. #15689184C2semidirect
15. C47×#520C2semidirect
182. #520D47semidirect
196. C47#3119semidirect